Given a matrix of n X n. The task is to calculate the absolute difference between the sums of its diagonal.
Examples:
Input : mat[][] = 11 2 4 4 5 6 10 8 -12 Output : 15 Sum of primary diagonal = 11 + 5 + (-12) = 4. Sum of primary diagonal = 4 + 5 + 10 = 19. Difference = |19 - 4| = 15. Input : mat[][] = 10 2 4 5 Output : 7
Calculate the sums across the two diagonals of a square matrix. Along the first diagonal of the matrix, row index = column index i.e mat[i][j] lies on the first diagonal if i = j. Along the other diagonal, row index = n – 1 – column index i.e mat[i][j] lies on the second diagonal if i = n-1-j. By using two loops we traverse the entire matrix and calculate the sum across the diagonals of the matrix.
Below is the implementation of this approach:
// C++ program to find the difference // between the sum of diagonal. #include <bits/stdc++.h> #define MAX 100 using namespace std;
int difference( int arr[][MAX], int n)
{ // Initialize sums of diagonals
int d1 = 0, d2 = 0;
for ( int i = 0; i < n; i++)
{
for ( int j = 0; j < n; j++)
{
// finding sum of primary diagonal
if (i == j)
d1 += arr[i][j];
// finding sum of secondary diagonal
if (i == n - j - 1)
d2 += arr[i][j];
}
}
// Absolute difference of the sums
// across the diagonals
return abs (d1 - d2);
} // Driven Program int main()
{ int n = 3;
int arr[][MAX] =
{
{11, 2, 4},
{4 , 5, 6},
{10, 8, -12}
};
cout << difference(arr, n);
return 0;
} |
Output:
15
Time Complexity: O(N*N), as we are using nested loops to traverse N*N times.
Auxiliary Space: O(1), as we are not using any extra space.
We can optimize above solution to work in O(n) using the patterns present in indexes of cells.
// C++ program to find the difference // between the sum of diagonal. #include <bits/stdc++.h> #define MAX 100 using namespace std;
int difference( int arr[][MAX], int n)
{ // Initialize sums of diagonals
int d1 = 0, d2 = 0;
for ( int i = 0; i < n; i++)
{
d1 += arr[i][i];
d2 += arr[i][n-i-1];
}
// Absolute difference of the sums
// across the diagonals
return abs (d1 - d2);
} // Driven Program int main()
{ int n = 3;
int arr[][MAX] =
{
{11, 2, 4},
{4 , 5, 6},
{10, 8, -12}
};
cout << difference(arr, n);
return 0;
} |
Output:
15
Time Complexity: O(N), as we are using a loop to traverse N times.
Auxiliary Space: O(1), as we are not using any extra space.
Please refer complete article on Find difference between sums of two diagonals for more details!